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(A) x > 3 (B) x ≤ 4 (C) -4< x < 4 (D) x > -4 (E) none of the above

\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?

Bunnel,

First of all, thank you very much.

The source of this questions is a bank of questions that I received from a friend, whose his teacher gave to him.

I have huge doubts on inequalities topics.

As you explained above any value X>-4 can satisfy this.

What is the best approach to deal with this kind of questions? I solved -3<x<5, but I could not figure out, X>-4 because -3>-4 and do not satisfy the inequality.

(A) x > 3 (B) x ≤ 4 (C) -4< x < 4 (D) x > -4 (E) none of the above

\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?

Bunnel,

First of all, thank you very much.

The source of this questions is a bank of questions that I received from a friend, whose his teacher gave to him.

I have huge doubts on inequalities topics.

As you explained above any value X>-4 can satisfy this.

What is the best approach to deal with this kind of questions? I solved -3<x<5, but I could not figure out, X>-4 because -3>-4 and do not satisfy the inequality.

(A) x > 3 (B) x ≤ 4 (C) -4< x < 4 (D) x > -4 (E) none of the above

\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?[/quote]

Hi, Bunuel Just wanted to ask that since in this question it is not mentioned that x is an integer, by the range x>-4 it will include values greater than -3 also (say -3.8) but our range is from -3 to 5 so isnt this wrong????

Hi, Bunuel Just wanted to ask that since in this question it is not mentioned that x is an integer, by the range x>-4 it will include values greater than -3 also (say -3.8) but our range is from -3 to 5 so isnt this wrong????

I tried to explain this in the post above.

We know that \(-3<x<5\). Any x from that range satisfy x > -4.

It's a tricky question, I think I've encountered a sort of this one in OG2017. Key to solve it is to find the range from the answer choices that covers all possible values of x,here it is answer choice D.

(A) x > 3 (B) x ≤ 4 (C) -4< x < 4 (D) x > -4 (E) none of the above

\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?

Hi Bunuel, thanks for the explanation. I tend to approach this questions in the wrong way, trying to find an answer choice that matches with the range found through the inequalities. For instance, in this case I was looking for -3<x<5 (or something more restrictive, such as -2 < x < -5), which led me to pick answer E.

Given your explanation, I understand that I should look for that condition that holds for every x in the range...but I still have a huge doubt. You say it is (D) x > -4 because any X from that range will be more than -4. Following your logic, wouldn't also B) x ≤ 4 be true? Our range is -3<x<5, which means that every x will be less or equal to 4.

(A) x > 3 (B) x ≤ 4 (C) -4< x < 4 (D) x > -4 (E) none of the above

\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?

Hi Bunuel, thanks for the explanation. I tend to approach this questions in the wrong way, trying to find an answer choice that matches with the range found through the inequalities. For instance, in this case I was looking for -3<x<5 (or something more restrictive, such as -2 < x < -5), which led me to pick answer E.

Given your explanation, I understand that I should look for that condition that holds for every x in the range...but I still have a huge doubt. You say it is (D) x > -4 because any X from that range will be more than -4. Following your logic, wouldn't also B) x ≤ 4 be true? Our range is -3<x<5, which means that every x will be less or equal to 4.

Is there something I am not getting right?

Your help is super appreciated

For \(-3<x<5\), (B) x ≤ 4 won't always be true. For example, x could be 4.5 (4.5 IS between -3 and 5) and in this case B is not true.
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